We shall take it as falsified only if we discover a reproducible effect which refutes the theory. Unfortunately, Polanyi did not get much attention from theorists of science, but his work was influential in some other fields.
More than one logically consistent construct can paint a usable likeness of the world, but there is no common ground from which to pit two against each other, theory against theory.
If something was observed in nature but no natural explanation for it was available at the time, then it was assumed that a natural explanation existed and could be found later. English philosopher A. Despite its straightforward name, the field is complex and remains an area of current inquiry.
It has been called by some "the most influential work of philosophy in the latter half of the 20th Century". Thus a few basic statements contradicting a theory will hardly induce us to reject it as falsified.
This led to efforts to derive mathematics solely from logic, especially the logic of set theory, and thereby disprove Kant's claim that mathematics is synthetic. Both sorts of entities enter our conceptions only as cultural posits.